Statistical and Biological Physics

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Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games

Tobias Reichenbach, Mauro Mobilia, and Erwin Frey

An astonishing biodiversity exists within the earth's ecosystems. While being of essential importance to the viability of ecological systems, conceptual explanations of such diversity pose major challenges. Indeed, in a naive understanding of Darwinian evolution, two interacting species would compete for resources until only the fitter one survives (competitive exclusion principle). Non-hierarchical competitions between species have been found to help resolving this apparent paradox, and promote biodiversity. The simplest form of such cyclic interactions is described by the game `rock-paper-scissors', where rock crushes scissors, scissors cut paper, and paper wraps rock in turn. Both experimentally as well as theoretically, in combination with spatial dispersal of static populations, such dynamics has been shown to guarantee stable coexistence of species. However, mobility is an important factor in most ecosystems, from animals that migrate from place to place to bacteria that swim and tumble. Using the rock-paper-scissors game to model interacting species, we demonstrate that mobility critically affects biodiversity. A threshold mobility exists such that above, some species go extinct, and only one survives. Below the threshold value, all species coexist in a stable manner by self-arranging into entangled, rotating spirals.

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